Subgroups — C₁₁×#7154 #14584347

Order 2816.

242 conjugacy classes of subgroups.

The subgroup lattice has 136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₁₁×C₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₁₁×#335	C₂	1	2	yes	maximal
3	C₂²×C₁₁×C₁₆	C₄	1	2	yes	—
4	C₂×C₁₁×C₄⋊C₈	—	2	2	no	—
5	C₂×C₄×C₈×C₁₁	C₂²	1	1	yes	characteristic
6	C₄×C₁₁×C₁₆	—	2	2	no	—
7	C₁₁×#335	—	2	2	no	—
8	C₁₁×#335	C₄	1	4	yes	—
9	C₂²×C₈×C₁₁	—	4	2	no	—
10	C₂²×C₈×C₁₁	C₂×C₄	1	1	yes	characteristic
11	C₂²×C₈×C₁₁	Q₈	1	1	yes	characteristic
12	C₂×C₄²×C₁₁	D₄	1	1	yes	characteristic
13	C₂×C₁₁×C₁₆	—	2	2	no	—
14	C₂×C₁₁×C₁₆	—	2	2	no	—
15	C₂×C₁₁×C₁₆	C₈	1	4	yes	complemented
16	C₁₁×C₄⋊C₈	—	2	4	no	—
17	C₁₁×C₄⋊C₈	—	4	2	no	—
18	C₄×C₈×C₁₁	C₂×C₄	1	2	yes	—
19	C₄×C₈×C₁₁	D₄	1	2	yes	—
20	#7154	C₁₁	1	1	yes	maximal, characteristic, direct product factor, Sylow
21	C₂²×C₄×C₁₁	C₄⋊C₄	1	1	yes	characteristic
22	C₂²×C₄×C₁₁	D₈	1	1	yes	characteristic
23	C₂²×C₄×C₁₁	Q₁₆	1	1	yes	characteristic
24	C₂×C₈×C₁₁	—	2	2	no	—
25	C₂×C₈×C₁₁	—	4	4	no	—
26	C₂×C₈×C₁₁	—	8	2	no	—
27	C₂×C₈×C₁₁	—	8	2	no	—
28	C₂×C₈×C₁₁	C₄²	1	1	yes	characteristic
29	C₂×C₈×C₁₁	C₂²⋊C₄	1	1	yes	characteristic
30	C₂×C₈×C₁₁	C₄⋊C₄	1	2	yes	—
31	C₂×C₈×C₁₁	C₂×C₈	1	2	yes	—
32	C₂×C₈×C₁₁	M₁₆	1	2	yes	—
33	C₄²×C₁₁	C₂²⋊C₄	1	2	yes	—
34	C₄²×C₁₁	SD₁₆	1	2	yes	—
35	C₁₁×C₁₆	—	2	4	no	—
36	C₂×C₄×C₁₆	C₂×C₁₁	1	1	yes	characteristic
37	C₂×#335	C₂×C₁₁	1	2	yes	—
38	C₂³×C₁₁	#107	1	1	yes	characteristic
39	C₂×C₄×C₁₁	—	2	2	no	—
40	C₂×C₄×C₁₁	#95	1	1	yes	characteristic
41	C₂×C₄×C₁₁	#102	1	2	yes	—
42	C₂×C₄×C₁₁	#103	1	2	yes	—
43	C₂×C₄×C₁₁	C₄⋊C₈	1	2	yes	—
44	C₂×C₄×C₁₁	#106	1	1	yes	characteristic
45	C₂×C₄×C₁₁	#108	1	2	yes	—
46	C₂×C₄×C₁₁	D₁₆	1	1	yes	characteristic
47	C₂×C₄×C₁₁	SD₃₂	1	2	yes	—
48	C₂×C₄×C₁₁	Q₃₂	1	1	yes	characteristic
49	C₈×C₁₁	—	2	2	no	—
50	C₈×C₁₁	—	8	4	no	—
51	C₈×C₁₁	C₄×C₈	1	1	yes	characteristic
52	C₈×C₁₁	#97	1	1	yes	characteristic
53	C₈×C₁₁	C₂²⋊C₈	1	2	yes	—
54	C₂²×C₁₆	C₄×C₁₁	1	2	yes	—
55	C₂×C₄⋊C₈	—	2	2	no	—
56	C₂×C₄×C₈	C₂²×C₁₁	1	1	yes	characteristic
57	C₄×C₁₆	—	2	2	no	—
58	#335	—	2	2	no	—
59	#335	C₄×C₁₁	1	4	yes	—
60	C₂²×C₁₁	#335	1	2	yes	—
61	C₂²×C₁₁	#340	1	1	yes	characteristic
62	C₂²×C₁₁	#366	1	1	yes	characteristic
63	C₂²×C₁₁	#367	1	1	yes	characteristic
64	C₂²×C₁₁	#368	1	2	yes	—
65	C₄×C₁₁	—	2	2	no	—
66	C₄×C₁₁	#334	1	2	yes	—
67	C₄×C₁₁	#336	1	1	yes	characteristic
68	C₄×C₁₁	#341	1	1	yes	characteristic
69	C₄×C₁₁	#357	1	2	yes	—
70	C₄×C₁₁	#358	1	2	yes	—
71	C₂²×C₈	—	4	2	no	—
72	C₂²×C₈	C₂×C₄×C₁₁	1	1	yes	characteristic
73	C₂²×C₈	Q₈×C₁₁	1	1	yes	characteristic
74	C₂×C₄²	D₄×C₁₁	1	1	yes	characteristic
75	C₂×C₁₆	—	2	2	no	—
76	C₂×C₁₆	—	2	2	no	—
77	C₂×C₁₆	C₈×C₁₁	1	4	yes	complemented
78	C₄⋊C₈	—	2	4	no	—
79	C₄⋊C₈	—	4	2	no	—
80	C₄×C₈	C₂×C₄×C₁₁	1	2	yes	—
81	C₄×C₈	D₄×C₁₁	1	2	yes	—
82	C₂×C₁₁	#1277	1	1	yes	characteristic
83	C₂×C₁₁	#1371	1	2	yes	—
84	C₂×C₁₁	#1372	1	2	yes	—
85	C₂×C₁₁	#1380	1	1	yes	characteristic
86	C₂×C₁₁	#1381	1	1	yes	characteristic
87	C₂²×C₄	C₁₁×C₄⋊C₄	1	1	yes	characteristic
88	C₂²×C₄	C₁₁×D₈	1	1	yes	characteristic
89	C₂²×C₄	C₁₁×Q₁₆	1	1	yes	characteristic
90	C₂×C₈	—	2	2	no	—
91	C₂×C₈	—	4	4	no	—
92	C₂×C₈	—	8	2	no	—
93	C₂×C₈	—	8	2	no	—
94	C₂×C₈	C₄²×C₁₁	1	1	yes	characteristic
95	C₂×C₈	C₁₁×C₂²⋊C₄	1	1	yes	characteristic
96	C₂×C₈	C₁₁×C₄⋊C₄	1	2	yes	—
97	C₂×C₈	C₂×C₈×C₁₁	1	2	yes	—
98	C₂×C₈	C₁₁×M₁₆	1	2	yes	—
99	C₄²	C₁₁×C₂²⋊C₄	1	2	yes	—
100	C₄²	C₁₁×SD₁₆	1	2	yes	—
101	C₁₆	—	2	4	no	—
102	C₁₁	#7154	1	1	yes	characteristic, direct product factor, Sylow
103	C₂³	C₁₁×#107	1	1	yes	characteristic
104	C₂×C₄	—	2	2	no	—
105	C₂×C₄	C₁₁×#95	1	1	yes	characteristic
106	C₂×C₄	C₁₁×#102	1	2	yes	—
107	C₂×C₄	C₁₁×#103	1	2	yes	—
108	C₂×C₄	C₁₁×C₄⋊C₈	1	2	yes	—
109	C₂×C₄	C₁₁×#106	1	1	yes	characteristic
110	C₂×C₄	C₁₁×#108	1	2	yes	—
111	C₂×C₄	C₁₁×D₁₆	1	1	yes	characteristic
112	C₂×C₄	C₁₁×SD₃₂	1	2	yes	—
113	C₂×C₄	C₁₁×Q₃₂	1	1	yes	characteristic
114	C₈	—	2	2	no	—
115	C₈	—	8	4	no	—
116	C₈	C₄×C₈×C₁₁	1	1	yes	characteristic
117	C₈	C₁₁×#97	1	1	yes	characteristic
118	C₈	C₁₁×C₂²⋊C₈	1	2	yes	—
119	C₂²	C₁₁×#335	1	2	yes	—
120	C₂²	C₁₁×#340	1	1	yes	characteristic
121	C₂²	C₁₁×#366	1	1	yes	characteristic
122	C₂²	C₁₁×#367	1	1	yes	characteristic
123	C₂²	C₁₁×#368	1	2	yes	—
124	C₄	—	2	2	no	—
125	C₄	C₁₁×#334	1	2	yes	—
126	C₄	C₁₁×#336	1	1	yes	characteristic
127	C₄	C₁₁×#341	1	1	yes	characteristic
128	C₄	C₁₁×#357	1	2	yes	—
129	C₄	C₁₁×#358	1	2	yes	—
130	C₂	C₁₁×#1277	1	1	yes	characteristic
131	C₂	C₁₁×#1371	1	2	yes	—
132	C₂	C₁₁×#1372	1	2	yes	—
133	C₂	C₁₁×#1380	1	1	yes	characteristic
134	C₂	C₁₁×#1381	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄×C₁₁	D₈
commutator	C₈	C₄×C₈×C₁₁
Frattini, cosocle	C₂×C₄×C₈	C₂²×C₁₁
socle, prime radical	C₂³×C₁₁	#107
LCS	G ▷ C₈ ▷ C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₄×C₁₁ ◁ C₂×C₄²×C₁₁ ◁ C₂×C₄×C₈×C₁₁ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
15. C₂×C₁₁×C₁₆	C₈	semidirect
20. #7154	C₁₁	direct (N × H)
77. C₂×C₁₆	C₈×C₁₁	semidirect
102. C₁₁	#7154	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₄×C₁₁×C₁₆	2
C₂×C₁₁×#335	2
#7154	11

Subgroups — C11×#7154 #14584347

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₁×#7154 #14584347